Covariance Calculator
How two variables move together, before standardising.
Enter your values
Enter the x values you are working with.
Enter the y values you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Sample covariance
- 13.5
- Population covariance
- 10.8
- Correlation r
- 0.98722
- Direction
- Positive — they rise together
- Mean of X / Y
- 6 / 8.8
- Sum of products
- 54
Quick answer
Covariance measures whether two variables move together: positive means they rise together, negative means one falls as the other rises.
cov = Σ(xᵢ − x̄)(yᵢ − ȳ) ÷ (n − 1)
At a glance
| What it does | How two variables move together, before standardising. |
|---|---|
| Category | Statistics |
| Inputs needed | X values, Y values |
| Main output | Sample covariance |
| Formula | cov = Σ(xᵢ − x̄)(yᵢ − ȳ) ÷ (n − 1) |
| Cost | Free — no sign-up, no download |
How to use the Covariance Calculator
- 1Enter the X values in order.
- 2Enter the matching Y values.
- 3Read covariance for direction and correlation for strength on a −1 to +1 scale.
Inputs explained
- X values
- Enter the x values you are working with.
- Y values
- Enter the y values you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- X values2, 4, 6, 8, 10
- Y values3, 7, 8, 12, 14
Results
- Sample covariance13.5
- Population covariance10.8
- Correlation r0.98722
- DirectionPositive — they rise together
- Mean of X / Y6 / 8.8
- Sum of products54
Frequently asked questions
Why is covariance hard to interpret?
Its size depends on the units — change metres to centimetres and covariance jumps 100-fold. Correlation fixes that.
Does zero covariance mean independence?
Not necessarily. It rules out a linear relationship, but a perfect U-shape can still have zero covariance.
What do I need to enter into the Covariance Calculator?
Just 2 values: x values, y values. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Covariance Calculator work out the answer?
Covariance measures whether two variables move together: positive means they rise together, negative means one falls as the other rises. It applies the formula cov = Σ(xᵢ − x̄)(yᵢ − ȳ) ÷ (n − 1) and shows the working so you can check each step by hand.
Is the Covariance Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.